Finite Group Databasebeta

← #16797427

Subgroups — #16797427

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719108C211yesmaximal, characteristic
2C2×#11719107C211yesmaximal, characteristic
3C4×#88240C211yesmaximal, characteristic, complemented
4C4×#88238C211yesmaximal, characteristic, complemented
5#13130656C211yesmaximal, characteristic, complemented
6#13130643C211yesmaximal, characteristic, complemented
7#13130640C211yesmaximal, characteristic, complemented
8#13130617C211yesmaximal, characteristic, complemented
9#13130615C211yesmaximal, characteristic, complemented
10#13130613C211yesmaximal, characteristic, complemented
11#13130611C211yesmaximal, characteristic, complemented
12#13130600C211yesmaximal, characteristic, complemented
13#13130599C211yesmaximal, characteristic, complemented
14#13130494C211yesmaximal, characteristic, complemented
15#13123631C211yesmaximal, characteristic
16C2×#88240C2211yescharacteristic
17C2×#88240C2211yescharacteristic
18C2×#88238C2211yescharacteristic
19C2×#88238C2211yescharacteristic
20C2×#88170C2211yescharacteristic
21C4×#6131C2211yescharacteristic
22C4×#6129C2211yescharacteristic
23C2×#88118C2211yescharacteristic
24C2×#88118C2211yescharacteristic
25C2×#88116C2211yescharacteristic
26C2×#88116C2211yescharacteristic
27C4×#6122—21no—
28C2×C4×#1057—21no—
29#11719108C418yescomplemented
30#11719107C418yescomplemented
31C2×#88104C2211yescharacteristic
32C2×#88103C2211yescharacteristic
33C2×#88100C2211yescharacteristic
34C2×#88100C2211yescharacteristic
35C2×C8×#261C2211yescharacteristic
36C2×C8×#261C2211yescharacteristic
37#11719072—21no—
38#11719072—21no—
39#11719072C2211yescharacteristic
40#11719072C2211yescharacteristic
41#11719072C2211yescharacteristic
42#11719072C2211yescharacteristic
43#11719062—21no—
44#11719062—21no—
45#11719057C2211yescharacteristic
46C4×#6118—21no—
47C4×#6118C2211yescharacteristic
48C4×#6118C2211yescharacteristic
49C4×D13⋊C8—21no—
50C4×D13⋊C8C2211yescharacteristic
51C13×#440C411yescharacteristic, complemented
52#11718825C411yescharacteristic, complemented
53#11718691C411yescharacteristic, complemented
54#11718675C411yescharacteristic, complemented
55#11718550C411yescharacteristic, complemented
56#11718541C2211yescharacteristic
57#11718465C2211yescharacteristic
58#11718450C411yescharacteristic, complemented
59#11718446C411yescharacteristic, complemented
60#11718433C2211yescharacteristic
61#11718371C411yescharacteristic, complemented
62D13×#97C2211yescharacteristic
63#11718268C2211yescharacteristic
64#11718268C2211yescharacteristic
65#11718247C2211yescharacteristic
66#11718247C2211yescharacteristic
67#11718247C2211yescharacteristic
68#11718247C2211yescharacteristic
69C2×#6131C2311yescharacteristic
70C2×#6129C2311yescharacteristic
71C2×#6122—21no—
72C2×#6122—21no—
73C22×#1057—21no—
74C22×#1057—21no—
75#88240—22no—
76#88240—22no—
77#88240C2×C414yescomplemented
78#88240C2×C414yescomplemented
79#88238—22no—
80#88238—22no—
81#88238C2×C414yescomplemented
82#88238C2×C414yescomplemented
83C2×C4×#261C2311yescharacteristic
84C2×C4×#261C2311yescharacteristic
85C2×#6118—21no—
86C2×#6118—21no—
87C2×#6118C2311yescharacteristic
88C2×#6118C2311yescharacteristic
89C2×#6118C2311yescharacteristic
90C2×#6118C2311yescharacteristic
91C2×D13⋊C8—21no—
92C2×D13⋊C8—21no—
93C2×D13⋊C8C2311yescharacteristic
94C2×D13⋊C8C2311yescharacteristic
95C2×C13×SD16C2×C411yescharacteristic
96C4×Q8×C13C2×C411yescharacteristic
97C4×D4×C13C2×C411yescharacteristic
98Q8×Dic13C2×C411yescharacteristic
99C2×#6107C2×C411yescharacteristic
100D4×Dic13C2×C411yescharacteristic
101C2×#6104C2×C411yescharacteristic
102C4×C22⋊D13—21no—
103C2×C4×Dic13—21no—
104#88170C2×C414yes—
105#88170C2×C414yes—
106C2×#6095C2×C411yescharacteristic
107C2×C8×D13C2311yescharacteristic
108C2×C8×D13C2311yescharacteristic
109#88147—21no—
110#88147C2×C411yescharacteristic
111#88146—21no—
112#88146C2311yescharacteristic
113#88146C2311yescharacteristic
114#88141C2×C411yescharacteristic
115#88135—21no—
116#88131—21no—
117C4×D52—21no—
118C4×D52C2×C411yescharacteristic
119C42×D13—21no—
120C42×D13C2311yescharacteristic
121C4×Dic26C2×C411yescharacteristic
122#88118C2×C414yescomplemented
123#88118C2×C414yescomplemented
124#88116C2×C414yescomplemented
125#88116C2×C414yescomplemented
126(C2×#261)⋊C4—21no—
127(C2×#261)⋊C4—21no—
128#88110—21no—
129#88110—21no—
130#88110—21no—
131#88110—21no—
132#88110—21no—
133#88110—21no—
134C4×#1057—21no—
135C4×#1057—21no—
136C4×#1057—21no—
137C4×#1057—21no—
138C4×#1057—21no—
139C4×#1057—21no—
140C4×#1057D411yescharacteristic
141C4×#1057D411yescharacteristic
142C4×#1057D411yescharacteristic
143C4×#1057D411yescharacteristic
144#88104C2×C414yescomplemented
145#88103C2×C414yescomplemented
146#88100—22no—
147#88100C2×C414yescomplemented
148C8×#261—22no—
149C8×#261C2×C414yescomplemented
150C13×#107C2×C411yescharacteristic
151C13×#103C2×C411yescharacteristic
152C13×#102C2×C411yescharacteristic
153C13×#97C2×C411yescharacteristic
154#88075C2×C411yescharacteristic
155#88072C2×C411yescharacteristic
156#88061C2×C411yescharacteristic
157#88058C2×C411yescharacteristic
158#88056C2×C411yescharacteristic
159#88055C2×C411yescharacteristic
160#88055C2×C411yescharacteristic
161#88050C2×C411yescharacteristic
162#88049C2×C411yescharacteristic
163#88048C2×C411yescharacteristic
164#88048C2×C411yescharacteristic
165#88043C2×C411yescharacteristic
166#20510—131nomaximal, Sylow
167C22×#261—21no—
168C22×#261—21no—
169C2×Q8×C13C22×C411yescharacteristic
170C2×D4×C13C22×C411yescharacteristic
171C22×C4×C13—21no—
172C2×C22⋊D13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175#6131—21no—
176#6131—21no—
177#6131C22×C412yes—
178#6131C22×C412yes—
179#6129—21no—
180#6129—21no—
181#6129C22×C412yes—
182#6129C22×C412yes—
183C2×D52—21no—
184C2×D52C22×C411yescharacteristic
185C2×C4×D13—21no—
186C2×C4×D13—21no—
187C2×C4×D13—21no—
188C2×C4×D13#4111yescharacteristic
189C2×C4×D13#4111yescharacteristic
190C2×C4×D13C2411yescharacteristic
191C2×Dic26C22×C411yescharacteristic
192#6122—24no—
193#6122—24no—
194C2×#1057—21no—
195C2×#1057—21no—
196C2×#1057—21no—
197C2×#1057—21no—
198C2×#1057—24no—
199C2×#1057—24no—
200C2×#1057C2×D411yescharacteristic
201C2×#1057C2×D411yescharacteristic
202C2×#1057C2×D411yescharacteristic
203C2×#1057C2×D411yescharacteristic
204C4×#261—21no—
205C4×#261—21no—
206C4×#261C22×C412yes—
207C4×#261C22×C412yes—
208#6118—21no—
209#6118—21no—
210#6118—21no—
211#6118—21no—
212#6118—24no—
213#6118—24no—
214#6118C22×C412yes—
215#6118C22×C412yes—
216#6118C22×C412yes—
217#6118C22×C412yes—
218D13⋊C8—24no—
219D13⋊C8—24no—
220D13⋊C8C22×C412yes—
221D13⋊C8C22×C412yes—
222D13⋊C8#4112yes—
223D13⋊C8#4112yes—
224C13×SD16C4214yes—
225C2×C8×C13C22×C411yescharacteristic
226C2×C8×C13C22×C411yescharacteristic
227C13×C4⋊C4—21no—
228C13×C4⋊C4C22×C411yescharacteristic
229C13×C4⋊C4C22×C411yescharacteristic
230C13×C22⋊C4—21no—
231C42×C13—21no—
232C42×C13C22×C411yescharacteristic
233C22⋊Dic13—21no—
234#6107C4214yes—
235#6104C4214yes—
236#6103—21no—
237#6103—21no—
238#6103—21no—
239#6103—21no—
240C4⋊Dic13—21no—
241C4⋊Dic13C22×C411yescharacteristic
242C4⋊Dic13C22×C411yescharacteristic
243#6101—21no—
244#6101—21no—
245C4×Dic13—21no—
246C4×Dic13—21no—
247C4×Dic13—21no—
248C4×Dic13—21no—
249C4×Dic13—21no—
250C4×Dic13C22×C411yescharacteristic
251C4×Dic13C2×D411yescharacteristic
252C4×Dic13C2×D411yescharacteristic
253C2×#1055C22×C411yescharacteristic
254C2×#1055C22×C411yescharacteristic
255#6095C4214yes—
256C8×D13—21no—
257C8×D13—21no—
258C8×D13C22×C412yes—
259C8×D13C22×C412yes—
260C2×#444—131no—
261C2×#443—131no—
262#2943—131no—
263C4×#131—131no—
264C4×#131—131no—
265#1778—131no—
266#1773—131no—
267#1772—131no—
268#1765—131no—
269#1765—131no—
270#1764—131no—
271#1764—131no—
272#1759—131no—
273#1759—131no—
274#1726—131no—
275C23×C13—21no—
276C22×D13—21no—
277C22×D13C2×#4111yescharacteristic
278C2×#261—22no—
279C2×#261—22no—
280C2×#261—41no—
281C2×#261—41no—
282C2×#261—41no—
283C2×#261—41no—
284Q8×C13—21no—
285Q8×C13C2×C4212yes—
286D4×C13—21no—
287D4×C13C2×C4212yes—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—42no—
292C2×C4×C13C4×D411yescharacteristic
293C2×C4×C13C4×D411yescharacteristic
294C2×C4×C13C23×C411yescharacteristic
295C22⋊D13—22no—
296C22⋊D13—22no—
297C2×Dic13—21no—
298C2×Dic13—22no—
299C2×Dic13—22no—
300C2×Dic13—21no—
301C2×Dic13—21no—
302C2×Dic13—42no—
303C2×Dic13C4×D411yescharacteristic
304C2×Dic13C4×D411yescharacteristic
305C2×Dic13C22×D411yescharacteristic
306D52—22no—
307D52—22no—
308D52—21no—
309D52C2×C4212yes—
310C4×D13—22no—
311C4×D13—22no—
312C4×D13—41no—
313C4×D13—41no—
314C4×D13—42no—
315C4×D13—42no—
316C4×D13C23×C411yescharacteristic
317C4×D13C23×C411yescharacteristic
318C4×D13C2×#4111yescharacteristic
319C4×D13C2×#4111yescharacteristic
320Dic26—21no—
321Dic26C2×C4212yes—
322#1057—22no—
323#1057—22no—
324#1057—22no—
325#1057—22no—
326#1057C4×D412yes—
327#1057C4×D412yes—
328#1057C4×D412yes—
329#1057C4×D412yes—
330C8×C13—21no—
331C8×C13C2×C4212yes—
332#1055—21no—
333#1055C2×C4212yes—
334C2×#135—131no—
335C2×#131—131no—
336C2×#131—131no—
337C2×#131—131no—
338C2×#131—131no—
339C4×#41—131no—
340C4×#41—131no—
341#444—138no—
342#443—138no—
343#442—131no—
344#442—131no—
345#441—131no—
346#441—131no—
347#440—131no—
348#440—131no—
349#440—131no—
350#440#26111yescharacteristic, complemented
351C2×#108—131no—
352C2×#108—131no—
353#427—131no—
354C2×#104—131no—
355C2×#104—131no—
356C2×#104—131no—
357C2×#104—131no—
358#416—131no—
359#416—131no—
360#405—131no—
361#405—131no—
362#405—131no—
363#405—131no—
364#405—261no—
365#405—261no—
366#405—261no—
367#405—261no—
368C4×M16—131no—
369C4×M16—131no—
370C4×M16—261no—
371C4×M16—261no—
372C2×#97—131no—
373C2×#97—131no—
374C2×#97—131no—
375C2×C4×C8—131no—
376C2×C4×C8—131no—
377C2×C4×C8—131no—
378C2×C4×C8—261no—
379C2×C4×C8—261no—
380#376—131no—
381#341—131no—
382#341—131no—
383#339—131no—
384#339—131no—
385#339—131no—
386#339—131no—
387C22×C13—22no—
388C22×C13—41no—
389C22×C13—41no—
390C22×C13C2×C4×D411yescharacteristic
391C2×D13—21no—
392C2×D13—21no—
393C2×D13—22no—
394C2×D13—41no—
395C2×D13—41no—
396C2×D13C4×#4111yescharacteristic
397C2×D13C4×#4111yescharacteristic
398#261—42no—
399#261—42no—
400C4×C13—21no—
401C4×C13—21no—
402C4×C13—22no—
403C4×C13—41no—
404C4×C13—41no—
405C4×C13C22×C4211yescharacteristic
406C4×C13C4×#4111yescharacteristic
407Dic13—21no—
408Dic13—21no—
409Dic13—22no—
410Dic13—41no—
411Dic13—41no—
412Dic13C2×C4×D411yescharacteristic
413Dic13C2×C4×D411yescharacteristic
414C2×#41—131no—
415C2×#41—131no—
416#135—134no—
417#135—134no—
418C2×Q16—131no—
419C2×SD16—131no—
420C2×SD16C2×#26111yescharacteristic
421C2×D8—131no—
422#131—134no—
423#131—134no—
424#131—134no—
425#131—134no—
426#131—262no—
427#131—262no—
428#131—262no—
429#131—262no—
430C2×M16—131no—
431C2×M16—131no—
432C2×M16—131no—
433C2×M16—131no—
434C2×M16—261no—
435C2×M16—261no—
436C2×M16—261no—
437C2×M16—261no—
438C22×C8—131no—
439C22×C8—131no—
440C22×C8—131no—
441C22×C8—131no—
442C22×C8—261no—
443C22×C8—261no—
444C22×C8—261no—
445C22×C8—261no—
446C4×Q8—131no—
447C4×Q8—131no—
448C4×Q8—131no—
449C4×Q8C2×#26111yescharacteristic
450C4×D4—131no—
451C4×D4—131no—
452C4×D4—131no—
453C4×D4—261no—
454C4×D4—261no—
455C4×D4—261no—
456C4×D4—261no—
457C4×D4C2×#26111yescharacteristic
458#117—131no—
459#117—131no—
460#117—261no—
461#117—261no—
462C2×C42—131no—
463C2×C42—131no—
464C2×C42—131no—
465C2×C42—261no—
466C2×C42—261no—
467#108—134no—
468#108—134no—
469#107—131no—
470#107C2×#26111yescharacteristic
471#106—131no—
472#106—131no—
473#104—134no—
474#104—134no—
475#104—134no—
476#104—134no—
477#103—131no—
478#103—131no—
479#103—131no—
480#103C2×#26111yescharacteristic
481#102—131no—
482#102—131no—
483#102—131no—
484#102C2×#26111yescharacteristic
485#97—134no—
486#97—131no—
487#97—131no—
488#97—131no—
489#97—261no—
490#97—261no—
491#97—262no—
492#97—261no—
493#97—261no—
494#97—261no—
495#97—261no—
496#97C2×#26111yescharacteristic
497C4×C8—134no—
498C4×C8—131no—
499C4×C8—131no—
500C4×C8—131no—
501C4×C8—131no—
502C4×C8—261no—
503C4×C8—261no—
504C4×C8—262no—
505C4×C8—261no—
506C4×C8—261no—
507C4×C8—261no—
508C4×C8—261no—
509#95—261no—
510#95—261no—
511C2×C13—42no—
512C2×C13C42×D411yescharacteristic
513C2×C13#295511yescharacteristic
514C2×C13#295511yescharacteristic
515D13—21no—
516D13—21no—
517D13—42no—
518#41—132no—
519#41—132no—
520#41—132no—
521#41—132no—
522#41—261no—
523#41—261no—
524#41—261no—
525#41—261no—
526C2×Q8—131no—
527C2×Q8C22×#26111yescharacteristic
528C2×D4—131no—
529C2×D4—261no—
530C2×D4—261no—
531C2×D4C22×#26111yescharacteristic
532C22×C4—21no—
533C22×C4—131no—
534C22×C4—131no—
535C22×C4—131no—
536C22×C4—261no—
537C22×C4—261no—
538C22×C4—261no—
539C22×C4—261no—
540C22×C4—261no—
541C22×C4—261no—
542C22×C4—261no—
543Q16—134no—
544SD16—134no—
545SD16C4×#26114yes—
546D8—134no—
547M16—132no—
548M16—132no—
549M16—132no—
550M16—132no—
551M16—264no—
552M16—264no—
553M16—264no—
554M16—264no—
555M16—261no—
556M16—261no—
557M16—261no—
558M16—261no—
559C2×C8—131no—
560C2×C8—131no—
561C2×C8—131no—
562C2×C8—131no—
563C2×C8—132no—
564C2×C8—132no—
565C2×C8—132no—
566C2×C8—132no—
567C2×C8—131no—
568C2×C8—132no—
569C2×C8—132no—
570C2×C8—131no—
571C2×C8—261no—
572C2×C8—261no—
573C2×C8—264no—
574C2×C8—264no—
575C2×C8—264no—
576C2×C8—264no—
577C2×C8—261no—
578C2×C8—261no—
579C2×C8—261no—
580C2×C8—261no—
581C2×C8C22×#26111yescharacteristic
582C2×C8C22×#26111yescharacteristic
583C4⋊C4—21no—
584C4⋊C4—131no—
585C4⋊C4—131no—
586C4⋊C4—261no—
587C4⋊C4—261no—
588C4⋊C4—261no—
589C4⋊C4C22×#26111yescharacteristic
590C4⋊C4C22×#26111yescharacteristic
591C22⋊C4—21no—
592C22⋊C4—261no—
593C22⋊C4—261no—
594C22⋊C4—261no—
595C22⋊C4—261no—
596C22⋊C4—261no—
597C42—21no—
598C42—131no—
599C42—131no—
600C42—131no—
601C42—132no—
602C42—132no—
603C42—261no—
604C42—261no—
605C42—261no—
606C42—261no—
607C42—261no—
608C42—261no—
609C42—261no—
610C42C22×#26111yescharacteristic
611C13#2051011yescharacteristic, complemented, Sylow
612C23—21no—
613C23—131no—
614C23—261no—
615Q8—21no—
616Q8—132no—
617Q8—261no—
618Q8C2×C4×#26112yes—
619D4—21no—
620D4—132no—
621D4—262no—
622D4—262no—
623D4—262no—
624D4—262no—
625D4—261no—
626D4C2×C4×#26112yes—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—42no—
631C2×C4—131no—
632C2×C4—131no—
633C2×C4—131no—
634C2×C4—131no—
635C2×C4—131no—
636C2×C4—131no—
637C2×C4—131no—
638C2×C4—262no—
639C2×C4—262no—
640C2×C4—262no—
641C2×C4—262no—
642C2×C4—261no—
643C2×C4—262no—
644C2×C4—262no—
645C2×C4—261no—
646C2×C4—261no—
647C2×C4—521no—
648C2×C4—521no—
649C2×C4—522no—
650C2×C4—522no—
651C2×C4—522no—
652C2×C4—521no—
653C2×C4—521no—
654C2×C4—521no—
655C2×C4—521no—
656C2×C4D4×#26111yescharacteristic
657C2×C4D4×#26111yescharacteristic
658C2×C4C23×#26111yescharacteristic
659C8—21no—
660C8—132no—
661C8—132no—
662C8—132no—
663C8—132no—
664C8—132no—
665C8—262no—
666C8—262no—
667C8—262no—
668C8—262no—
669C8—261no—
670C8C2×C4×#26112yes—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—131no—
675C22—131no—
676C22—261no—
677C22—261no—
678C22—262no—
679C22—521no—
680C22—521no—
681C22C2×D4×#26111yescharacteristic
682C4—22no—
683C4—21no—
684C4—21no—
685C4—41no—
686C4—41no—
687C4—131no—
688C4—131no—
689C4—262no—
690C4—261no—
691C4—261no—
692C4—522no—
693C4—522no—
694C4—521no—
695C4—521no—
696C4C22×C4×#26111yescharacteristic
697C4#41×#26111yescharacteristic
698C2—42no—
699C2—261no—
700C2—261no—
701C2—522no—
702C2C4×D4×#26111yescharacteristic
703C2#1313160811yescharacteristic
704C2#1313160911yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC13×#440C4
socleC22×C13C2×C4×D4
prime radicalC2×#88170C22
cosocleC2×C4×D13C24
hypercenter#440#261
hypocenterC13#20510
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C4×#88240C2semidirect
4. C4×#88238C2semidirect
5. #13130656C2semidirect
6. #13130643C2semidirect
7. #13130640C2semidirect
8. #13130617C2semidirect
9. #13130615C2semidirect
10. #13130613C2semidirect
11. #13130611C2semidirect
12. #13130600C2semidirect
13. #13130599C2semidirect
14. #13130494C2semidirect
29. #11719108C4semidirect
30. #11719107C4semidirect
51. C13×#440C4semidirect
52. #11718825C4semidirect
53. #11718691C4semidirect
54. #11718675C4semidirect
55. #11718550C4semidirect
58. #11718450C4semidirect
59. #11718446C4semidirect
61. #11718371C4semidirect
77. #88240C2×C4semidirect
78. #88240C2×C4semidirect
81. #88238C2×C4semidirect
82. #88238C2×C4semidirect
122. #88118C2×C4semidirect
123. #88118C2×C4semidirect
124. #88116C2×C4semidirect
125. #88116C2×C4semidirect
144. #88104C2×C4semidirect
145. #88103C2×C4semidirect
147. #88100C2×C4semidirect
149. C8×#261C2×C4semidirect
350. #440#261semidirect
611. C13#20510semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117191082
C2×#117191072
C4×#882402
C4×#882382
#131306562
#131306432
#131306402
#131306172
#131306152
#131306132
#131306112
#131306002
#131305992
#131304942
#131236312
#2051013